5edo: Difference between revisions
Wikispaces>jdfreivald **Imported revision 233282612 - Original comment: Added commas tempered out.** |
Wikispaces>jdfreivald **Imported revision 233338490 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 21:32:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>233338490</tt>.<br> | ||
: The revision comment was: <tt> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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||= 2889416/2882415 ||> 4.200 || Vulture || || || | 24 -21 4 > || | ||= 2889416/2882415 ||> 4.200 || Vulture || || || | 24 -21 4 > || | ||
||= 36/35 ||> 48.770 || Septimal Quarter Tone || || || | 2 2 -1 -1 > || | ||= 36/35 ||> 48.770 || Septimal Quarter Tone || || || | 2 2 -1 -1 > || | ||
||= 49/48 ||> 35.697 || Slendro Diesis || || || | -4 -1 2 > || | ||= 49/48 ||> 35.697 || Slendro Diesis || || || | -4 -1 0 2 > || | ||
||= 64/63 ||> 27.264 || Septimal Comma || Archytas' Comma || Leipziger Komma || | 6 -2 0 -1 > || | ||= 64/63 ||> 27.264 || Septimal Comma || Archytas' Comma || Leipziger Komma || | 6 -2 0 -1 > || | ||
||= 245/243 ||> 14.191 || Sensamagic || || || | -5 1 2 > || | ||= 245/243 ||> 14.191 || Sensamagic || || || | 0 -5 1 2 > || | ||
||= 1728/1715 ||> 13.074 || Orwellisma || Orwell Comma || || | 6 3 -1 -3 > || | ||= 1728/1715 ||> 13.074 || Orwellisma || Orwell Comma || || | 6 3 -1 -3 > || | ||
||= 1029/1024 ||> 8.433 || Gamelisma || || || | -10 1 0 3 > || | ||= 1029/1024 ||> 8.433 || Gamelisma || || || | -10 1 0 3 > || | ||
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||= 1065875/1063543 ||> 3.792 || Wadisma || || || | -26 -1 1 9 > || | ||= 1065875/1063543 ||> 3.792 || Wadisma || || || | -26 -1 1 9 > || | ||
||= 420175/419904 ||> 1.117 || Wizma || || || | -6 -8 2 5 > || | ||= 420175/419904 ||> 1.117 || Wizma || || || | -6 -8 2 5 > || | ||
||= 99/98 ||> 17.576 || Mothwellsma || || || | -1 2 -2 1 > || | ||= 99/98 ||> 17.576 || Mothwellsma || || || | -1 2 0 -2 1 > || | ||
||= 896/891 ||> 9.688 || Pentacircle || || || | 7 -4 0 1 -1 > || | ||= 896/891 ||> 9.688 || Pentacircle || || || | 7 -4 0 1 -1 > || | ||
||= 385/384 ||> 4.503 || Keenanisma || || || | -7 -1 1 1 1 > || | ||= 385/384 ||> 4.503 || Keenanisma || || || | -7 -1 1 1 1 > || | ||
||= 441/440 ||> 3.930 || Werckisma || || || | -3 2 -1 2 -1 > || | ||= 441/440 ||> 3.930 || Werckisma || || || | -3 2 -1 2 -1 > || | ||
||= 3025/3024 ||> 0.572 || Lehmerisma || || || | -4 -3 2 -1 2 > || | ||= 3025/3024 ||> 0.572 || Lehmerisma || || || | -4 -3 2 -1 2 > || | ||
||= 91/90 ||> 19.130 || Superleap || || || | -1 -2 -1 1 1 > || | ||= 91/90 ||> 19.130 || Superleap || || || | -1 -2 -1 1 0 1 > || | ||
||= 676/675 ||> 2.563 || Parizeksma || || || | 2 -3 -2 2 > || | ||= 676/675 ||> 2.563 || Parizeksma || || || | 2 -3 -2 0 0 2 > || | ||
|| < 5 8 12 14 17 19 | || | || < 5 8 12 14 17 19 | ||</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>5edo</title></head><body><!-- ws:start:WikiTextTocRule:28:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#x5 Equal Divisions of the Octave: Theory">5 Equal Divisions of the Octave: Theory</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#x5-edo in Musicmaking">5-edo in Musicmaking</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>5edo</title></head><body><!-- ws:start:WikiTextTocRule:28:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#x5 Equal Divisions of the Octave: Theory">5 Equal Divisions of the Octave: Theory</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#x5-edo in Musicmaking">5-edo in Musicmaking</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | ||
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Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain <a class="wiki_link" href="/Bug%20family">bug temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as 1-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.<br /> | Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain <a class="wiki_link" href="/Bug%20family">bug temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as 1-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.<br /> | ||
<br /> | <br /> | ||
Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See <!-- ws:start:WikiTextUrlRule: | Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See <!-- ws:start:WikiTextUrlRule:684:http://www.research.att.com/~njas/sequences/A117538 --><a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a><!-- ws:end:WikiTextUrlRule:684 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2> | ||
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<td>| -4 -1 2 &gt;<br /> | <td>| -4 -1 0 2 &gt;<br /> | ||
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<td><br /> | <td><br /> | ||
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<td>| -5 1 2 &gt;<br /> | <td>| 0 -5 1 2 &gt;<br /> | ||
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<td><br /> | <td><br /> | ||
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<td>| -1 2 -2 1 &gt;<br /> | <td>| -1 2 0 -2 1 &gt;<br /> | ||
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<td><br /> | <td><br /> | ||
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<td>| -1 -2 -1 1 1 &gt;<br /> | <td>| -1 -2 -1 1 0 1 &gt;<br /> | ||
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<td><br /> | <td><br /> | ||
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<td>| 2 -3 -2 2 &gt;<br /> | <td>| 2 -3 -2 0 0 2 &gt;<br /> | ||
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</tr> | </tr> | ||
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</table> | </table> | ||
</body></html></pre></div> | |||